Party meaning “a specific individual” is old in the language, going back to the 15th century, and was formerly in common use. Today, it remains standard in limited senses, chiefly the legal, and is often used humorously or condescendingly: the party holding the balloon. The word person is the neutral and common term.

party

n.

late 13c., "part, portion, side," from Old French partie "side, part; portion, share; separation, division" (12c.), literally "that which is divided," noun use of fem. past participle of partir "to divide" (see part (v.)). Political sense of "side in a contest or dispute" evolved by 1300; meaning "a person" is from mid-15c. Sense of "gathering for social pleasure" is first found 1716, from general sense of persons gathered together (originally for some specific purpose, e.g. dinner party, hunting party). Phrase the party is over is from 1937; party line is first recorded 1834 in the sense of "policy adopted by a political party," 1893 in the sense of "telephone line shared by two or more subscribers." Party pooper is from 1951, American English.

v.

"have a good time," 1922, from party (n.). Earlier as "to take the side of" (1630s). Related: Partied; partying.